Question

If A(–1, 0), B(5, –2) and C(8, 2) are the vertices of a ΔABC then its centroid is ______.

Options

• (12, 0)

• (6, 0)

• (0, 6)

• (4, 0)

Answer 1

If A(–1, 0), B(5, –2) and C(8, 2) are the vertices of a ΔABC then its centroid is (4, 0).

Explanation:

The centroid G of triangle with vertices A(x₁, y₁), B(x₂, y₂), C(x₃, y₃) has coordinates `G((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`.

Here `x = (-1 + 5 + 8)/3`

= `12/3`

= 4

And `y = (0 + (-2) + 2)/3`

= `0/3`

= 0

So, G = (4, 0).